Question

find the measure of \\( \angle qtn \\).
\\( m \angle qtn = \\) \\( \circ \\)

Explanation:

Step1: Use the property of corresponding angles

Since \( OP\parallel QR\), then \((2x + 55)^{\circ}=(7x + 25)^{\circ}\) (corresponding angles are equal).

$$\begin{align*} 2x+55&=7x + 25\\ 55-25&=7x-2x\\ 30&=5x\\ x& = 6 \end{align*}$$

Step2: Calculate \(m\angle QTN\)

Substitute \(x = 6\) into \((7x + 25)^{\circ}\).
\(7x+25=7\times6 + 25=42+25 = 67\)

Answer:

\(67\)